Limiting Absorption Principle for Stratified Operators with Thresholds: A General Method |
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Authors: | B Vainberg & Marc Durand |
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Institution: | 1. University of Provence , CMI, 39 rue Joliot-Curie, Marseilles Cedex 13 , 13453 , France mdurand@cmi.univ-mrs.fr |
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Abstract: | Out problem is about propagation of waves in stratified strips. The operators are quite general, a typical example being a coupled elasto-acoustic operator H defined in ?2 × I where I is a bounded interval of ? with coefficients depending only on z ∈ I. The “conjugate operator method” will be applied to an operator obtained by a spectral decomposition of the partial Fourier transform ? of H. Around each value of the spectrum (except the eigenvalues) including the thresholds, a conjugate operator is constructed which permits to get the ”good properties“ of regularity for H. A limiting absorption principle is then obtained for a large class of operators at every point of the spectrum (except eigenvalues). |
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Keywords: | Limiting absorption principle Multistratified layers Coupled operators |
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